Despite the fact that topological phases are defined at the ground state at equilibrium, quantum quenches in recent studies provide nonequilibrium way to investigate topological physics [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}. Particularly, as a momentum-space counterpart of the bulk-boundary correspondence, the dynamical bulk-surface correspondence was proposed [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, which relates the bulk topology of an equilibrium phase to nontrivial dynamical topological phase emerging on certain momentum subspaces called band-inversion surfaces (BISs) when quenching the system across topological transitions. This dynamical topology enables a broadly applicable way to characterize and detect topological phases by quantum dynamics, and has triggered many experimental studies in quantum simulations, such as in ultracold atoms [22]}, [23]}, nitrogen-vacancy defects in diamond [24]}, [25]}, [26]}, nuclear magnetic resonance (NMR) [27]}, and superconducting circuits [28]}.
